Linear Algebra Examples

$[\begin{array}{c} 8 & - 7 & 2 & 3 & 7 & - 1 & 0 \\ 9 & - 3 & 1 & 2 & 1 & - 2 & - 4 \end{array}] + [\begin{array}{c} 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ - 1 & - 5 & - 4 & 9 & - 2 & - 3 & 0 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 8 + 1 & - 7 + 2 & 2 + 3 & 3 + 4 & 7 + 5 & - 1 + 6 & 0 + 7 \\ 9 - 1 & - 3 - 5 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $8$ and $1$ .

$[\begin{array}{c} 9 & - 7 + 2 & 2 + 3 & 3 + 4 & 7 + 5 & - 1 + 6 & 0 + 7 \\ 9 - 1 & - 3 - 5 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.2

Add $- 7$ and $2$ .

$[\begin{array}{c} 9 & - 5 & 2 + 3 & 3 + 4 & 7 + 5 & - 1 + 6 & 0 + 7 \\ 9 - 1 & - 3 - 5 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.3

Add $2$ and $3$ .

$[\begin{array}{c} 9 & - 5 & 5 & 3 + 4 & 7 + 5 & - 1 + 6 & 0 + 7 \\ 9 - 1 & - 3 - 5 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.4

Add $3$ and $4$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 7 + 5 & - 1 + 6 & 0 + 7 \\ 9 - 1 & - 3 - 5 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.5

Add $7$ and $5$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & - 1 + 6 & 0 + 7 \\ 9 - 1 & - 3 - 5 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.6

Add $- 1$ and $6$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & 5 & 0 + 7 \\ 9 - 1 & - 3 - 5 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.7

Add $0$ and $7$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & 5 & 7 \\ 9 - 1 & - 3 - 5 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.8

Subtract $1$ from $9$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & 5 & 7 \\ 8 & - 3 - 5 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.9

Subtract $5$ from $- 3$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & 5 & 7 \\ 8 & - 8 & 1 - 4 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.10

Subtract $4$ from $1$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & 5 & 7 \\ 8 & - 8 & - 3 & 2 + 9 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.11

Add $2$ and $9$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & 5 & 7 \\ 8 & - 8 & - 3 & 11 & 1 - 2 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.12

Subtract $2$ from $1$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & 5 & 7 \\ 8 & - 8 & - 3 & 11 & - 1 & - 2 - 3 & - 4 + 0 \end{array}]$

Step 2.13

Subtract $3$ from $- 2$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & 5 & 7 \\ 8 & - 8 & - 3 & 11 & - 1 & - 5 & - 4 + 0 \end{array}]$

Step 2.14

Add $- 4$ and $0$ .

$[\begin{array}{c} 9 & - 5 & 5 & 7 & 12 & 5 & 7 \\ 8 & - 8 & - 3 & 11 & - 1 & - 5 & - 4 \end{array}]$